The present invention relates to active and passive sensor applications, and more particularly is directed to efficient systems and methods for detection and tracking of one or more targets.
Detection and tracking of targets by sensor systems have been the subject matter of a large number of practical applications. Sensor systems designed for this purpose may use propagating wave signals, such as electromagnetic or acoustical signals. Some sensor systems, such as radar and active sonar systems, are designed to receive reflections of a transmitted signal generated by an appropriate conventional transmitter. This type of sensor systems will be referred to as active sensor systems. In contrast with the active sensor systems, in many cases sensor systems are designed to receive signals not generated by a cooperating transmitter. Such sensor systems will be referred to next as passive sensor systems.
Active sensor systems are generally used for detection of scattering objects that show great variation in size and type. In the presence of a scattering object, the transmitted signal arrives to the receiving sensor system with a certain time delay, which is related to the range of the scattering object (i.e., the distance to it). Also, if the scattering object is moving, the reflected signal exhibits a spectral shift that is known as a Doppler shift. The Doppler shift is related to the relative velocity of the object with respect to the sensor system. In order to provide an example of a received signal in an active sensor system, a simulation has been conducted for a radar system that transmits a phase-coded radar signal as shown in FIG. 1A. In this simulation, the transmitted signal reflects back from an object, at a 12 km range, which is moving with a velocity of 400 m/s towards the radar system. The reflected signal is received by the radar antenna and down-converted by a conventional analog receiver system, such as shown in FIG. 4. The output of the analog receiver system is shown in FIG. 1B, where the effects of the object range and velocity are seen as a delay and an additional frequency modulation of the received signal, respectively. These two prominent effects of the received signal can be more readily observable on the cross-ambiguity function of the transmitted and received signals, which is defined as:
Ar,s(xcfx84,xcexd)=∫r(t+xcfx84/2)s*(txe2x88x92xcfx84/2)ej2xcfx80vtdtxe2x80x83xe2x80x83(1.1)
where s(t) is the transmitted signal and r(t) is the received signal. For the transmitted and received signal pair shown in FIGS. 1A and 1B, respectively, the magnitude of the cross-ambiguity function is illustrated in FIG. 1C as a 3-Dimensional plot. In FIG. 1D, the contour plot of the same cross-ambiguity function is provided. Since it is easier to visualize the structure, contour plots of the cross-ambiguity function are more commonly used in practice. As seen in FIG. 1D, the peak of the cross-ambiguity function is located at the corresponding delay and Doppler shift caused by the scattering object. This observed correspondence between the peak location of the cross-ambiguity function on one hand, and the position and the velocity of the scattering object on the other is a general relationship, which holds true in all cases where there is no or little noise at the receiver.
In the case of a noisy reception of the reflected signal, the peak location of the cross-ambiguity function still provides a reliable estimate of the delay and the Doppler shift caused by the scattering object [1]. Therefore, in accordance with the present invention it is possible to detect the presence of a scattering object by finding the peak locations of the cross-ambiguity function and comparing them with appropriately chosen threshold levels. Those peaks that exceed the thresholds can be identified as scattering objects, and the locations of the peaks will provide the corresponding delay and Doppler shift information at the same time.
Although the use of the cross-ambiguity function for detection of scattering objects and estimation of their corresponding delay and Doppler shifts is known in the prior art, this approach has only been used in sophisticated sensor systems because of the high cost and difficulty of implementation. Therefore, in most of the applications where the cost is a critical issue, the sensor systems are designed to detect the presence of scattering objects and estimate either their range or their velocities, but not both. The main objective of the present invention in relation to active sensor systems is to provide an efficient and low-cost system and method that can reliably detect scattering objects and estimate both their delay and their Doppler shifts at the same time.
Passive sensor systems are generally used for the interception of signals emitted by transmitters that are not in cooperation with the sensor system, i.e., operate independently of it. Unlike the active sensor systems where the range and the velocity of the objects can be estimated from the reflected signals, passive sensor systems cannot decide on the range and the velocity of the intercepted transmitter without extensive prior information about the transmitter. In passive reception, the main purpose is the detection of an existing transmitter. Once a transmitter is detected, its intercepted signal can be analyzed to obtain information about the type and purpose of the transmitter. This information generally plays a crucial role in determining what type of action should be taken in the presence of the detected transmitter. FIG. 2A shows a frequency-modulated signal, which is an example of an intercepted signal by a passive sensor system. The instantaneous frequency of this signal varies in time, as shown in FIG. 2C. The intercepted signal is down-converted by a conventional analog receiver system as shown, for example, in FIG. 4. The output of the analog receiver system is shown in FIG. 2B, where synthetic noise is added to simulate an actual noisy reception. As seen from FIG. 2B, the detection of the signal can be a difficult task, especially for intercepted signals that have low amplitudes. Therefore, in cases where the detection of weaker signals in noise is extremely important, such as in early warning applications, more sophisticated detection algorithms are required. Similar to the case of active sensor systems, in accordance with the present invention reliable detection of signals in noise can be performed in the ambiguity-function domain by computing the auto-ambiguity function of the down-converted received signal as follows:
Ar(xcfx84,xcexd)=∫r(t+xcfx84/2)r*(txe2x88x92xcfx84/2)ej2xcfx80vtdtxe2x80x83xe2x80x83(1.2)
where r(t) is the received signal. The noisy received signal is shown in FIG. 2C, and its corresponding auto-ambiguity function is shown in FIG. 2D. As seen in FIG. 2D, the intercepted signal is easily detectable in this plot. However, in practice the auto-ambiguity function approach is almost never used in the detection of intercepted signals due to the associated high cost and complexity. The main objective of the present invention in relation to the passive sensor systems is to provide an efficient and low-cost method and algorithm that makes use of the auto-ambiguity function for reliable detection and classification of intercepted signals.
The interested reader is directed to the disclosure of the following publications, which are incorporated by reference for additional background. Reference numerals used in the following description correspond to the numbering in the listing below.
[1] P. M. Woodward, Probability and Information Theory, with Applications to Radar, New York: Pergamino Press Inc., 1953.
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Additional information is also provided in U.S. Pat. Nos. 5,760,732; 5,657,022; 5,583,505; 5,548,157 and 5,457,462, which are incorporated herein by reference.
The present invention is based on the simultaneous computation of distance and Doppler shift information using fast computation of the ambiguity function and/or Wigner distribution of received signals along on arbitrary line. By using the fractional Fourier transformation of time domain signals, closed form expressions for arbitrary projections of their auto or cross ambiguity function are derived. By utilizing discretization of the obtained analytical expressions, efficient algorithms are proposed in accordance to the present invention to compute uniformly spaced samples of the Wigner distribution and the ambiguity function located on arbitrary line segments. With repeated use of the proposed algorithms, in alternative embodiments of the invention, samples in the Wigner or ambiguity domain can be computed on non-Cartesian sampling grids, such as polar grids, which are the natural sampling grids of chirp-like signals. The ability to obtain samples of the Wigner distribution and ambiguity function over both rectangular and polar grids is potentially useful in a wide variety of application areas, including time-frequency domain kernel design, multicomponent signal analysis, time-frequency domain signal detection and particle location analysis in Fresnel holograms.